Learning graphical models with hidden variables can offer semantic insights to complex data and lead to salient structured predictors without relying on expensive, sometime unattainable fully annotated training data. While likelihood-based methods have been extensively explored, to our knowledge, learning structured prediction models with latent variables based on the max-margin principle remains largely an open problem. In this paper, we present a partially observed Maximum Entropy Discrimination Markov Network (PoMEN) model that attempts to combine the advantages of Bayesian and margin based paradigms for learning Markov networks from partially labeled data. PoMEN leads to an averaging prediction rule that resembles a Bayes predictor that is more robust to overfitting, but is also built on the desirable discriminative laws resemble those of the M$^3$N. We develop an EM-style algorithm utilizing existing convex optimization algorithms for M$^3$N as a subroutine. We demonstrate competent performance of PoMEN over existing methods on a real-world web data extraction task.

Kernel supervised learning methods can be unified by utilizing the tools from regularization theory. The duality between regularization and prior leads to interpreting regularization methods in terms of maximum a posteriori estimation and has motivated Bayesian interpretations of kernel methods. In this paper we pursue a Bayesian interpretation of sparsity in the kernel setting by making use of a mixture of a point-mass distribution and prior that we refer to as ``Silverman's g-prior.'' We provide a theoretical analysis of the posterior consistency of a Bayesian model choice procedure based on this prior. We also establish the asymptotic relationship between this procedure and the Bayesian information criterion.

We develop new techniques for time series classification based on hierarchical Bayesian generative models (called mixed-effect models) and the Fisher kernel derived from them. A key advantage of the new formulation is that one can compute the Fisher information matrix despite varying sequence lengths and varying sampling intervals. This avoids the commonly-used ad hoc replacement of the Fisher information matrix with the identity which destroys the geometric invariance of the kernel. Our construction retains the geometric invariance, resulting in a kernel that is properly invariant under change of coordinates in the model parameter space. Experiments on detecting cognitive decline show that classifiers based on the proposed kernel outperform those based on generative models and other feature extraction routines, and on Fisher kernels that use the identity in place of the Fisher information.

Detecting underlying clusters from large-scale data plays a central role in machine learning research. In this paper, we attempt to tackle clustering problems for complex data of multiple distributions and large multi-scales. To this end, we develop an algorithm named Zeta $l$-links, or Zell which consists of two parts: Zeta merging with a similarity graph and an initial set of small clusters derived from local $l$-links of the graph. More specifically, we propose to structurize a cluster using cycles in the associated subgraph. A mathematical tool, Zeta function of a graph, is introduced for the integration of all cycles, leading to a structural descriptor of the cluster in determinantal form. The popularity character of the cluster is conceptualized as the global fusion of variations of the structural descriptor by means of the leave-one-out strategy in the cluster. Zeta merging proceeds, in the agglomerative fashion, according to the maximum incremental popularity among all pairwise clusters. Experiments on toy data, real imagery data, and real sensory data show the promising performance of Zell. The $98.1\%$ accuracy, in the sense of the normalized mutual information, is obtained on the FRGC face data of 16028 samples and 466 facial clusters. The MATLAB codes of Zell will be made publicly available for peer evaluation.

In this paper, we address the question of what kind of knowledge is generally transferable from unlabeled text. We suggest and analyze the semantic correlation of words as a generally transferable structure of the language and propose a new method to learn this structure using an appropriately chosen latent variable model. This semantic correlation contains structural information of the language space and can be used to control the joint shrinkage of model parameters for any specific task in the same space through regularization. In an empirical study, we construct 190 different text classification tasks from a real-world benchmark, and the unlabeled documents are a mixture from all these tasks. We test the ability of various algorithms to use the mixed unlabeled text to enhance all classification tasks. Empirical results show that the proposed approach is a reliable and scalable method for semi-supervised learning, regardless of the source of unlabeled data, the specific task to be enhanced, and the prediction model used.

Many machine learning algorithms can be formulated in the framework of statistical independence such as the Hilbert Schmidt Independence Criterion. In this paper, we extend this criterion to deal with with structured and interdependent observations. This is achieved by modeling the structures using undirected graphical models and comparing the Hilbert space embeddings of distributions. We apply this new criterion to independent component analysis and sequence clustering.

Multi-level hierarchical models provide an attractive framework for incorporating correlations induced in a response variable organized in a hierarchy. Model fitting is challenging, especially for hierarchies with large number of nodes. We provide a novel algorithm based on a multi-scale Kalman filter that is both scalable and easy to implement. For non-Gaussian responses, quadratic approximation to the log-likelihood results in biased estimates. We suggest a bootstrap strategy to correct such biases. Our method is illustrated through simulation studies and analyses of real world data sets in health care and online advertising.

In partially observable worlds with many agents, nested beliefs are formed when agents simultaneously reason about the unknown state of the world and the beliefs of the other agents. The multi-agent filtering problem is to efficiently represent and update these beliefs through time as the agents act in the world. In this paper, we formally define an infinite sequence of nested beliefs about the state of the world at the current time $t$ and present a filtering algorithm that maintains a finite representation which can be used to generate these beliefs. In some cases, this representation can be updated exactly in constant time; we also present a simple approximation scheme to compact beliefs if they become too complex. In experiments, we demonstrate efficient filtering in a range of multi-agent domains.

The cluster assumption is exploited by most semi-supervised learning (SSL) methods. However, if the unlabeled data is merely weakly related to the target classes, it becomes questionable whether driving the decision boundary to the low density regions of the unlabeled data will help the classification. In such case, the cluster assumption may not be valid; and consequently how to leverage this type of unlabeled data to enhance the classification accuracy becomes a challenge. We introduce Semi-supervised Learning with Weakly-Related Unlabeled Data" (SSLW), an inductive method that builds upon the maximum-margin approach, towards a better usage of weakly-related unlabeled information. Although the SSLW could improve a wide range of classification tasks, in this paper, we focus on text categorization with a small training pool. The key assumption behind this work is that, even with different topics, the word usage patterns across different corpora tends to be consistent. To this end, SSLW estimates the optimal word-correlation matrix that is consistent with both the co-occurrence information derived from the weakly-related unlabeled documents and the labeled documents. For empirical evaluation, we present a direct comparison with a number of state-of-the-art methods for inductive semi-supervised learning and text categorization; and we show that SSLW results in a significant improvement in categorization accuracy, equipped with a small training set and an unlabeled resource that is weakly related to the test beds."

Regularized Least Squares (RLS) algorithms have the ability to avoid over-fitting problems and to express solutions as kernel expansions. However, we observe that the current RLS algorithms cannot provide a satisfactory interpretation even on a constant function. On the other hand, while kernel-based algorithms have been developed in such a tendency that almost all learning algorithms are kernelized or being kernelized, a basic fact is often ignored: The learned function from the data and the kernel fits the data well, but may not be consistent with the kernel. Based on these considerations and on the intuition that a good kernel-based inductive function should be consistent with both the data and the kernel, a novel learning scheme is proposed. The advantages of this scheme lie in its corresponding Representer Theorem, its strong interpretation ability about what kind of functions should not be penalized, and its promising accuracy improvements shown in a number of experiments. Furthermore, we provide a detailed technical description about heat kernels, which serves as an example for the readers to apply similar techniques for other kernels. Our work provides a preliminary step in a new direction to explore the varying consistency between inductive functions and kernels under various distributions.